Value functions are a core component of reinforcement learning systems. The main idea is to to construct a single function approximator V (s; θ) that estimates the long-term reward from any state s, using parameters θ. In this paper we introduce universal value function approximators (UVFAs) V (s, g; θ) that generalise not just over states s but also over goals g. We develop an efficient techni...

The existing uncertainties during the operation of processes could strongly affect performance forecasting systems, control strategies and fault detection systems when they are not considered in design. Because that, study uncertainty quantification has gained more attention among researchers past decades. From this field study, prediction intervals arise as one techniques most used literature ...

The success of reinforcement learning in practical problems depends on the ability to combine function approximation with temporal di erence methods such as value iteration. Experiments in this area have produced mixed results; there have been both notable successes and notable disappointments. Theory has been scarce, mostly due to the difculty of reasoning about function approximators that gen...

Unlike the conventional neural network theories and implementations, Huang et al. [Universal approximation using incremental constructive feedforward networks with random hidden nodes, IEEE Transactions on Neural Networks 17(4) (2006) 879–892] have recently proposed a new theory to show that single-hidden-layer feedforward networks (SLFNs) with randomly generated additive or radial basis functi...

In 1989 Hornik as well as Funahashi established that multilayer feedforward networks without the squashing function in the output layer are universal approximators. This result has been often used improperly because it has been applied to multilayer feedforward networks with the squashing function in the output layer. In this paper, we will prove that also this kind of neural networks are unive...

A key element in the solution of reinforcement learning problems is the value function The purpose of this function is to measure the long term utility or value of any given state The function is important because an agent can use this measure to decide what to do next A common problem in reinforcement learning when applied to systems having continuous states and action spaces is that the value...

In this paper, we consider a fundamental theoretical question: Is it always possible to design a fuzzy system able of approximating any real continuous function on a compact set with arbitrary accuracy? Moreover, we will research whether the answer to the above question is positive when we restrict to a fixed (but arbitrary) type of fuzzy reasoning and to a subclass of fuzzy relations. This res...

In many real-life situations, we do not know the actual dependence y = f(x1, . . . , xn) between the physical quantities xi and y, we only know expert rules describing this dependence. These rules are often described by using imprecise (“fuzzy”) words from natural language. Fuzzy techniques have been invented with the purpose to translate these rules into a precise dependence y = f̃(x1, . . . , ...